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Topic: Pochhammer symbol

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	Combining Presentation and Content Markup
		For instance, the factorial of a number might be expressed with an exclamation mark, a Gamma function, or a Pochhammer symbol.
		Thus, in a presentation context, elements such as these do not have a clearly defined meaning, and hence there is no obvious choice for a rendering.
		Using the terminology of Section 4.2.1 Overview of Syntax and Usage, we see that operator, relation, container, constant and symbol elements make sense on their own, while elements of the qualifier and condition type do not.
	www.w3.org /TR/MathML2/chapter5.html (3690 words)

	Pochhammer symbol - Wikipedia, the free encyclopedia
		In mathematics, the Pochhammer symbol, introduced by Leo August Pochhammer,
		The study of similarities of this type is known as umbral calculus.
		The general theory covering such relations, including the Pochhammer polynomials, is given by the theory of polynomial sequences of binomial type and by Sheffer sequences.
	en.wikipedia.org /wiki/Pochhammer_symbol (353 words)

	Symbol (Site not responding. Last check: 2007-10-18)
		Symbols Of the Mathematics Of the LÃ¡tex. Prepared by L. Kocbach, in base of this document (origin: David Carlisle, University Of Manchester).
		The program of the symbol of the SOLDIER ENLISTED IN the ARMY is a labeled program of of the food for the foods of carbohydrate that have had their value of index glycemic determined and satisfies specific...
		The symbol of Pearson indicates the crystalline symmetry and the number of atoms in the note of the unit...
	symbol.like8march.com (2943 words)

	Pochhammer symbol: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-18)
		Note that the falling factorial can be written as a binomial coefficient In mathematics, in particular in combinatorics, the binomial coefficient of the natural number n and the integer k is defined to be the natural number...
		The rising factorial can be generalized to a continuous value of n using the Gamma function In mathematics, the gamma function is a function that extends the concept of factorial to the complex numbers....
		The general theory covering such relations, including the Pochhammer polynomials, is given by the theory of polynomial sequences of binomial type In mathematics, a polynomial sequence, i.e., a sequence of polynomials indexed by 0, 1, 2, 3,......
	www.absoluteastronomy.com /u/pochhammer_symbol (580 words)

	Facts about symbol (Site not responding. Last check: 2007-10-18)
		A word, for example, is a symbol of language which references its own definition.
		It is human beings' ability to manipulate symbols that allows them to explore the relationships between ideas, things, concepts, and qualities -- far beyond the explorations of which any other species on earth is capable.
		Religious and metaphysical writings are also known for their use of esoteric symbolism, as is Freudian psychoanalysis.
	www.supercrawler.com /Facts/symbol.html (153 words)

	Hypergeometric Series, Hypergeometric Function - Numericana
		Pochhammer's symbol: Upper factorial of k increasing factors, starting with x.
		is called a Pochhammer symbol in honor of Leo August Pochhammer (1841-1920) who introduced generalized hypergeometric functions in 1870.
		It is customary to indicate the value of p and q as subscripts before and after the symbol F. These unnecessary subscripts improve readability, but they are often dropped in the case of Gauss's original function.
	home.att.net /~numericana/answer/hyper.htm (459 words)

	infofx.info - Permutation (Site not responding. Last check: 2007-10-18)
		A permutation is an ordered sequence containing each symbol from a set once and only once; neither "1, 2, 2, 3, 4, 5, 6" nor "1, 2, 4, 5, 6" are permutations.
		However, the same notation is used for the rising factorial (also called Pochhammer symbol) :n(n + 1)(n + 2)...(n + r − 1).
		The lowercase Iota symbol is sometimes used to write the imaginary unit but more often latin i or latin j are used.
	sword.of.honour.en.infofx.info /en/permutation (3956 words)

	GNU Scientific Library -- Reference Manual - Gamma Function (Site not responding. Last check: 2007-10-18)
		These routines compute the Pochhammer symbol @math{(a)_x := \Gamma(a + x)/\Gamma(x)}, subject to @math{a} and @math{a+x} not being negative integers.
		These routines compute the logarithm of the Pochhammer symbol, @math{\log((a)_x) = \log(\Gamma(a + x)/\Gamma(a))} for @math{a > 0}, @math{a+x > 0}.
		These routines compute the sign of the Pochhammer symbol and the logarithm of its magnitude.
	www.math.utah.edu /software/gsl/gsl-ref_114.html (574 words)

	Hypergeometric series: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-18)
		The series, if convergent, will define a hypergeometric function which may then be defined over a wider domain of the argument by analytic continuation In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function....
		where is the rising factorial or Pochhammer symbol In mathematics, the pochhammer symbol, introduced by leo august pochhammer,...
		Since Pochhammer notation In mathematics, the pochhammer symbol, introduced by leo august pochhammer,...
	www.absoluteastronomy.com /h/hypergeometric_series (1710 words)

	Pochhammer symbol : Pockhammer symbol (Site not responding. Last check: 2007-10-18)
		terms defined : Pochhammer symbol : Pockhammer symbol
		In mathematics, the Pochhammer symbol $(x)_n\,$ is used in the theory of special functions to represent the "rising factorial" or "upperfactorial" $(x)_n=x(x+1)(x+2)\cdots(x+n-1)$ and, confusingly, is used in combinatorics to represent the "falling factorial" or "lower factorial" $(x)_n=x(x-1)(x-2)\cdots(x-n+1).$
		He and the Dry-Salters seemed to have wrought a sort of.
	www.termsdefined.net /po/pockhammer-symbol.html (341 words)

	C157-3-22 (Site not responding. Last check: 2007-10-18)
		I don't expect you to understand this, but you should be able to program it.
		The Pochhammer symbol can be though of as a generalization of the factorial function.
		(Pochhammer of a and n) and by (b)
	www.lasalle.edu /~blum/c157wks/c157-3-22.htm (118 words)

	pochhammer symbol - OneLook Dictionary Search (Site not responding. Last check: 2007-10-18)
		We found 3 dictionaries with English definitions that include the word pochhammer symbol:
		Tip: Click on the first link on a line below to go directly to a page where "pochhammer symbol" is defined.
		Pochhammer Symbol : Eric Weisstein's World of Mathematics [home, info]
	www.onelook.com /?w=pochhammer+symbol (81 words)

	Math Markup Language (Chapter 5)
		Thus, the same presentation markup can be rendered with relative ease on screen in either wide and narrow windows, in ASCII or graphics, in print, or it can be enunciated in a sensible way when spoken.
		we use the mo presentation element inside a ci element to achieve the proper presentation, along with a semantics element which binds a semantic definition to the symbol.
		Here, the semantics of the presentation subexpressions have been given using symbols from OpenMath content dictionaries (CD).
	www.w3.org /TR/REC-MathML/chapter5.html (2031 words)

	[No title]
		BeginPackage["NewZeil`"] Print["This is the Mathematica Package NewZeil"]; Print["version 0.99, 12 April 2005"]; Print["written by Andrew Sills"]; Print["to accompany the paper"]; Print["`Sharp Upper Bounds for the Orders of the Recurrences Output by the Zeilberger and q-Zeilberger Algorithms'"]; Print["by Mohamud Mohammed and Doron Zeilberger"]; Print["J. Symbolic Comput., 39 (2005), 201-207.
		The notation used in coding and documenting this package intentionally follows that of Mohammed and Zeilberger's paper `Sharp upper bounds...', JSC 39, 201-207 as closely as possible.
		" rf::usage = "rf[a,n] is an abbreviation for the standard Mathematica symbol Pochhammer[a,n]." Zeil::usage= "Zeil[H, z, POL, k, n, params], where H is the pure hypergeometric part of 'ProperHypergeometric' less the argument z (i.e.
	www.math.rutgers.edu /~asills/mathematica/NewZeil.m (284 words)

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